Donor- and acceptor-type (D/A) impurities play central roles in controlling the physical properties of semiconductors. With continued miniaturization of information processing devices, the relationship between quantum confinement and D/A ionization energies becomes increasingly important. Here, we provide direct spectroscopic evidence that impurity D/A levels in doped semiconductor nanostructures are energetically pinned, resulting in variations in D/A binding energies with increasing quantum confinement. Using magnetic circular dichroism spectroscopy, the donor binding energies of Co2+ ions in colloidal ZnSe quantum dots have been measured as a function of quantum confinement and analyzed in conjunction with ab initio density functional theory calculations. The resulting experimental demonstration of pinned impurity levels in quantum dots has far-reaching implications for physical phenomena involving impurity-carrier interactions in doped semiconductor nanostructures, including in the emerging field of semiconductor spintronics where magnetic-dopant-carrier exchange interactions define the functionally relevant properties of diluted magnetic semiconductors.